How Azure or AWS will be beneficial in my current architecture?

I am working on a software, which stores user’s data (mostly PDFs, Few video files etc.).

To maintain it, I have account on Swift Cloud. Now, To manage many multiple users and their data in GBs/TBs, I am having a facility of 6-8 servers which continuously collects users request of uploading their data and upload it on cloud. Most of these servers are busy doing this all the time.

The problem which I face in this outdated architecture –

  1. It is very time consuming process to upload a particular file and since user enter a lot of data, it takes a considerable amount of time. (in hours/days sometime)
  2. Maintaining servers and load distribution is also a tedious task now.
  3. Need few developers dedicated to this process in case any issue occurs.
  4. Slow data upload and download.
  5. If a file having a smaller size, and another file prior it having a big size. Then the small file needs to wait until the large file gets uploaded.

I am having thousands of users, Many of them are facing these above issues. I am sure their are solutions to these problem based on famous cloud computing like AWS and Azure, But I am not very much clear about them if they can solve these issue and if yes, then how and what should be the action should I suggest to my upper management.

P.S. – In current architecture, We are using C#.